cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A344025 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j) and A003557(i) = A003557(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 17, 18, 19, 20, 2, 21, 2, 22, 23, 24, 25, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 35, 36, 37, 38, 2, 39, 28, 40, 41, 21, 2, 42, 2, 43, 44, 45, 46, 47, 2, 48, 49, 50, 2, 51, 2, 52, 53, 54, 46, 55, 2, 56, 57, 58, 2, 59, 41, 60, 61, 62, 2, 63, 37, 64
Offset: 1

Views

Author

Antti Karttunen, May 07 2021

Keywords

Comments

Restricted growth sequence transform of the ordered pair [A003415(n), A003557(n)], where A003415(n) is the arithmetic derivative of n, and A003557(n) is n divided by its largest squarefree divisor.
For all i, j:
parent(i) = parent(j) => a(i) = a(j),
a(i) = a(j) => A342001(i) = A342001(j),
a(i) = a(j) => A369051(i) = A369051(j) => A085731(i) = A085731(j).
Where "parent" can be any of the sequences A351236, A351260, A353520, A353521, A369050, for example.

Links

Crossrefs

Cf. A003415, A003557, A085731, A342001, A369051.
Cf. also A305800, A351236, A351260, A353520, A353521, A369050, and also A353523.

Programs

  • PARI
    up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
Aux344025(n) = [A003415(n), A003557(n)];
v344025 = rgs_transform(vector(up_to, n, Aux344025(n)));
A344025(n) = v344025[n];

A353521 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A003557(i) = A003557(j) and A000035(i) = A000035(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 11, 12, 3, 13, 3, 14, 15, 16, 3, 17, 18, 19, 20, 21, 3, 22, 3, 23, 24, 25, 26, 27, 3, 28, 29, 30, 3, 31, 3, 32, 33, 34, 3, 35, 36, 37, 38, 39, 3, 40, 29, 41, 42, 22, 3, 43, 3, 44, 45, 46, 47, 48, 3, 49, 50, 51, 3, 52, 3, 53, 54, 55, 47, 56, 3, 57, 58, 59, 3, 60, 42, 61, 62, 63, 3, 64, 38
Offset: 1

Views

Author

Antti Karttunen, Apr 27 2022

Keywords

Comments

Restricted growth sequence transform of the triplet [A003415(n), A003557(n), A000035(n)].
For all i, j:
A305801(i) = A305801(j) => A353520(i) = A353520(j) => a(i) = a(j),
a(i) = a(j) => A007814(i) = A007814(j),
a(i) = a(j) => A344025(i) = A344025(j),
a(i) = a(j) => A353522(i) = A353522(j).

Links

Crossrefs

Cf. A000035, A003415, A003557, A007814.
Cf. also A305801, A344025, A351260, A353520, A353522.

Programs

  • PARI
    up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A000035(n) = (n%2);
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
Aux353521(n) = [A003415(n), A003557(n), A000035(n)];
v353521 = rgs_transform(vector(up_to,n,Aux353521(n)));
A353521(n) = v353521[n];

A353522 Lexicographically earliest infinite sequence such that a(i) = a(j) => A000035(i) = A000035(j) and A003415(i) = A003415(j), for all i, j >= 1, where A000035 and A003415 compute the parity and the arithmetic derivative of their argument.

Original entry on oeis.org

1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 11, 12, 3, 13, 3, 14, 15, 16, 3, 17, 15, 18, 19, 12, 3, 20, 3, 21, 22, 23, 24, 25, 3, 13, 26, 27, 3, 28, 3, 29, 30, 31, 3, 32, 22, 33, 34, 35, 3, 36, 26, 37, 38, 20, 3, 37, 3, 39, 40, 41, 42, 43, 3, 44, 45, 46, 3, 47, 3, 48, 49, 21, 42, 50, 3, 51, 52, 53, 3, 54, 38, 33, 55, 56, 3, 57, 34, 58
Offset: 1

Views

Author

Antti Karttunen, Apr 27 2022

Keywords

Comments

Restricted growth sequence transform of the ordered pair [A000035(n), A003415(n)].
For all i, j:
A353520(i) = A353520(j) => A353521(i) = A353521(j) => a(i) = a(j).

Links

Crossrefs

Cf. A000035, A003415.
Cf. also A305801, A353520, A353521.

Programs

  • PARI
    up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A000035(n) = (n%2);
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
Aux353522(n) = [A000035(n), A003415(n)];
v353522 = rgs_transform(vector(up_to,n,Aux353522(n)));
A353522(n) = v353522[n];

A361021 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(i) = A007814(j), A001065(i) = A001065(j) and A051953(i) = A051953(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 11, 12, 3, 13, 3, 14, 15, 16, 3, 17, 18, 19, 20, 21, 3, 22, 3, 23, 24, 25, 26, 27, 3, 28, 29, 30, 3, 31, 3, 32, 33, 34, 3, 35, 36, 37, 38, 39, 3, 40, 29, 41, 42, 43, 3, 44, 3, 45, 46, 47, 48, 49, 3, 50, 51, 52, 3, 53, 3, 54, 55, 56, 48, 57, 3, 58, 59, 60, 3, 61, 42, 62, 63, 64, 3, 65, 38, 66, 67, 68, 69, 70, 3, 71
Offset: 1

Views

Author

Antti Karttunen, Mar 03 2023

Keywords

Comments

Restricted growth sequence transform of the triplet [A007814(n), A001065(n), A051953(n)].
For all i, j >= 1:
A305801(i) = A305801(j) => a(i) = a(j),
a(i) = a(j) => A305895(i) = A305895(j),
a(i) = a(j) => A319346(i) = A319346(j).

Links

Crossrefs

Cf. A001065, A007814, A051953.
Cf. A305801, A305895, A319346.
Cf. also A353560.
Differs from A353520 for the first time at n=254, where a(254) = 187, while A353520(254) = 125.

Programs

  • PARI
    up_to = 100000;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A007814(n) = valuation(n,2);
A001065(n) = (sigma(n)-n);
A051953(n) = (n-eulerphi(n));
Aux361021(n) = [A007814(n), A001065(n), A051953(n)];
v361021 = rgs_transform(vector(up_to,n,Aux361021(n)));
A361021(n) = v361021[n];

A373980 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A003415(n), A085731(n), A181819(n), A373247(n)], for all i, j >= 1.

Original entry on oeis.org

1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 11, 12, 3, 13, 3, 14, 15, 16, 3, 17, 18, 19, 20, 21, 3, 22, 3, 23, 24, 25, 26, 27, 3, 28, 29, 30, 3, 31, 3, 32, 33, 34, 3, 35, 36, 37, 38, 39, 3, 40, 29, 41, 42, 43, 3, 44, 3, 45, 46, 47, 48, 49, 3, 50, 51, 52, 3, 53, 3, 54, 55, 56, 48, 57, 3, 58, 59, 60, 3, 61, 42, 62, 63, 64, 3, 65, 38, 66, 67, 68, 69, 70, 3, 71, 72
Offset: 1

Views

Author

Antti Karttunen, Jun 24 2024

Keywords

Comments

Restricted growth sequence transform of the quadruple [A003415(n), A085731(n), A181819(n), A373247(n)].
For all i, j >= 1:
A305801(i) = A305801(j) => a(i) = a(j),
a(i) = a(j) => A300249(i) = A300249(j) => A101296(i) = A101296(j),
a(i) = a(j) => A369051(i) = A369051(j),
a(i) = a(j) => A373250(i) = A373250(j).

Links

Crossrefs

Cf. A003415, A085731, A181819, A373247.
Cf. A101296, A300249, A305801, A369051, A373250.
Differs from A353520 and A361021 first at n=130, where a(130) = 82, while A353520(130) = A361021(130) = 96.

Programs

  • PARI
    up_to = 100000;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
Aux373980(n) = { my(d=A003415(n), s=A181819(n)); [d, s, gcd(n,d), n%s]; };
v373980 = rgs_transform(vector(up_to, n, Aux373980(n)));
A373980(n) = v373980[n];

A361026 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003557(i) = A003557(j) and A053669(i) = A053669(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 1, 3, 1, 4, 1, 5, 6, 2, 1, 7, 1, 2, 1, 8, 1, 9, 1, 3, 1, 2, 1, 10, 11, 2, 12, 3, 1, 13, 1, 14, 1, 2, 1, 15, 1, 2, 1, 5, 1, 4, 1, 3, 6, 2, 1, 16, 17, 18, 1, 3, 1, 19, 1, 5, 1, 2, 1, 20, 1, 2, 6, 21, 1, 4, 1, 3, 1, 2, 1, 22, 1, 2, 11, 3, 1, 4, 1, 8, 23, 2, 1, 7, 1, 2, 1, 5, 1, 24, 1, 3, 1, 2, 1, 25, 1, 26, 6, 27, 1, 4, 1, 5, 1
Offset: 1

Views

Author

Antti Karttunen, Mar 03 2023

Keywords

Comments

Restricted growth sequence transform of the ordered pair [A003557(n), A053669(n)].
For all i, j >= 1,
A305801(i) = A305801(j) => A353520(i) = A353520(j) => a(i) = a(j),
a(i) = a(j) => A007814(i) = A007814(j).

Links

Crossrefs

Cf. A003557, A007814, A053669.
Cf. A305801, A353520.

Programs

  • PARI
    up_to = 100000;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A003557(n) = (n/factorback(factorint(n)[, 1]));
A053669(n) = forprime(p=2, , if(n%p, return(p))); \\ From A053669
Aux361026(n) = [A003557(n), A053669(n)];
v361026 = rgs_transform(vector(up_to,n,Aux361026(n)));
A361026(n) = v361026[n];
Showing 1-6 of 6 results.

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